1) How did Inquisitors find Atium mistings?
2) Before, Inquisitors had supernatural healing. How did they get the Feruchemists for the spike? Were the keepers not so hidden after all?
3) And this is more towards the whole physics stuff, but is Feruchemy really balanced? If it gives diminishing returns, wouldn't this end up as a net loss of power?
4) How much control do allomancers have over pushing and pulling metals?
1) They spike the drinks at one of the nobility's balls with trace amounts of Atium, then cause a bit disturbance. (Often, the Inquisitors themselves arriving will do it) and burn bronze and watch for brief pulses. The body will burn metals instinctively if it can, which has been shown quite often in the series. This is also how they get a lot of their secret information about who is a Misting and who isn't. It's not a perfect method, since you have to watch for Copperclouds messing things up, but it is effective once in a while.
Any time an obligator who is not a Misting joins the Ministry, he is unknowingly given a larger chunk of atium and then forced into a series of rituals that will drain him physically and get the body to react and burn the metal. This was how Yomen was discovered.
2) The keepers have been hunted for years. Much like skaa Allomancers, they were often captured and taken by the Inquisitors. It didn't happen nearly as often, of course. Two things to remember, however: Not all Inquisitors had the same spikes, and spikes CAN be reused with much less effectiveness. The longer they are outside of a body, the more their power degrades.
3) It doesn't diminish. Or, well, it does--but only if you compound it. You get 1 for 1 back, but compounding the power requires an expenditure of the power itself. For instance, if you are weak for one hour, you can gain the lost strength for one hour. But that's not really that much strength. After all, you probably weren't as weak as zero people during that time. So if you want to be as strong as two men, you couldn't do it for a full hour. You'd have to spend some energy to compound, then spend the compounded energy itself.
In more mathematical terms, let's say you spend one hour at 50% strength. You could then spend one hour at 150% strength, or perhaps 25 min at 200% strength, or maybe 10min at 250% strength. Each increment is harder, and therefore 'strains' you more and burns your energy more quickly. And since most Feruchemists don't store at 50% strength, but instead at something like 80% strength (it feels like much more when they do it, but you can't really push the body to that much forced weakness without risking death) you can burn through a few day's strength in a very short time if you aren't careful.
4) Depends on the Allomancer. Zane and Kelsier were both unusually skilled in this area, and represent the higher end of what is possible.